Table Of Content

i QUANTITATIVE METHODS FOR BUSINESS AND MANAGEMENT QCF Level 5 Unit Contents Chapter Title Page Introduction to the Study Manual v Unit Specification (Syllabus) vii Coverage of the Syllabus by the Manual xi Formulae and Tables Provided with the Examination Paper xiii 1 Data and Data Collection 1 Introduction 2 Measurement Scales and Types of Data 3 Collecting Primary Data 5 Collecting Secondary Data 10 2 Sampling Procedures 13 Introduction 14 Statistical Inference 15 Sampling 16 Sampling Methods 18 Choice of Sampling Method 23 3 Tabulating and Graphing Frequency Distributions 25 Introduction 26 Frequency Distributions 27 Class Limits and Class Intervals 29 Cumulative and Relative Frequency Distributions 31 Ways of Presenting Frequency Distributions 34 Presenting Cumulative Frequency Distributions 40 4 Measures of Location 43 Introduction 44 Use of Measures of Location 45 Means 46 Median 51 Quantiles 54 Mode 57 Choice of Measure 58 Appendix: Functions, Equations and Graphs 60 © ABE ii Chapter Title Page 5 Measures of Dispersion 67 Introduction 68 Range 69 Quartile Deviation 70 Standard Deviation and Variance 72 Coefficient of Variation 75 Skewness 76 6 Index Numbers 79 Introduction 80 Simple (Unweighted) Index Numbers 80 Weighted index Numbers (Laspeyres and Paasche Indices) 83 Fisher's Ideal Index 85 Formulae 86 Quantity or Volume Index Numbers 87 Changing the Index Base Year 90 Index Numbers in Practice 91 7 Correlation 99 Introduction 100 Scatter Diagrams 100 The Correlation Coefficient 104 Rank Correlation 108 8 Linear Regression 113 Introduction 114 Regression Lines 115 Use of Regression 119 Connection Between Correlation and Regression 119 Multiple Regression 120 9 Time Series Analysis 121 Introduction 122 Structure of a Time Series 122 Calculation of Component Factors for the Additive Model 126 Multiplicative Model 135 Forecasting 139 The Z Chart 141 10 Probability 143 Introduction 145 Two Laws of Probability 146 Permutations 149 Combinations 152 Conditional Probability 154 Sample Space 155 Venn Diagrams 157 © ABE iii Chapter Title Page 11 Binomial and Poisson Distributions 173 Introduction 174 The Binomial Distribution 175 Applications of the Binomial Distribution 182 Mean and Standard Deviation of the Binomial Distribution 184 The Poisson Distribution 184 Application of the Poisson Distribution 186 Poisson Approximation to a Binomial Distribution 188 Application of Binomial and Poisson Distributions – Control Charts 191 Appendix: The Binomial Expansion 199 12 The Normal Distribution 201 Introduction 202 The Normal Distribution 202 Use of the Standard Normal Table 206 General Normal Probabilities 208 Use of Theoretical Distributions 210 Appendix: Areas in the Right-hand Tail of the Normal Distribution 214 13 Significance Testing 215 Introduction 216 Introduction to Sampling Theory 217 Confidence Intervals 219 Hypothesis Tests 221 Significance Levels 228 Small Sample Tests 229 14 Chi-squared Tests 235 Introduction 236 Chi-squared as a Test of Independence 236 Chi-squared as a Test of Goodness of Fit 241 Appendix: Area in the Right Tail of a Chi-squared (2) Distribution 245 15 Decision-making 247 Introduction 248 Decision-making Under Certainty 248 Definitions 249 Decision-making Under Uncertainty 250 Decision-making Under Risk 252 Complex Decisions 255 16 Applying Mathematical Relationships to Economic and Business 261 Problems Using Linear Equations to Represent Demand and Supply Functions 262 The Effects of a Sales Tax 267 Breakeven Analysis 269 Breakeven Charts 271 The Algebraic Representation of Breakeven Analysis 275 © ABE iv © ABE v Introduction to the Study Manual Welcome to this study manual for Quantitative Methods for Business And Management. The manual has been specially written to assist you in your studies for this QCF Level 5 Unit and is designed to meet the learning outcomes listed in the unit specification. As such, it provides thorough coverage of each subject area and guides you through the various topics which you will need to understand. However, it is not intended to "stand alone" as the only source of information in studying the unit, and we set out below some guidance on additional resources which you should use to help in preparing for the examination. The syllabus from the unit specification is set out on the following pages. This has been approved at level 4 within the UK's Qualifications and Credit Framework. You should read this syllabus carefully so that you are aware of the key elements of the unit – the learning outcomes and the assessment criteria. The indicative content provides more detail to define the scope of the unit. Following the unit specification is a breakdown of how the manual covers each of the learning outcomes and assessment criteria. After the specification and breakdown of the coverage of the syllabus, we also set out the additional material which will be supplied with the examination paper for this unit. This is provided here for reference only, to help you understand the scope of the specification, and you will find the various formulae and rules given there fully explained later in the manual. The main study material then follows in the form of a number of chapters as shown in the contents. Each of these chapters is concerned with one topic area and takes you through all the key elements of that area, step by step. You should work carefully through each chapter in turn, tackling any questions or activities as they occur, and ensuring that you fully understand everything that has been covered before moving on to the next chapter. You will also find it very helpful to use the additional resources (see below) to develop your understanding of each topic area when you have completed the chapter. Additional resources  ABE website – www.abeuk.com. You should ensure that you refer to the Members Area of the website from time to time for advice and guidance on studying and on preparing for the examination. We shall be publishing articles which provide general guidance to all students and, where appropriate, also give specific information about particular units, including recommended reading and updates to the chapters themselves.  Additional reading – It is important you do not rely solely on this manual to gain the information needed for the examination in this unit. You should, therefore, study some other books to help develop your understanding of the topics under consideration. The main books recommended to support this manual are listed on the ABE website and details of other additional reading may also be published there from time to time.  Newspapers – You should get into the habit of reading the business section of a good quality newspaper on a regular basis to ensure that you keep up to date with any developments which may be relevant to the subjects in this unit.  Your college tutor – If you are studying through a college, you should use your tutors to help with any areas of the syllabus with which you are having difficulty. That is what they are there for! Do not be afraid to approach your tutor for this unit to seek clarification on any issue as they will want you to succeed!  Your own personal experience – The ABE examinations are not just about learning lots of facts, concepts and ideas from the study manual and other books. They are also about how these are applied in the real world and you should always think how the © ABE vi topics under consideration relate to your own work and to the situation at your own workplace and others with which you are familiar. Using your own experience in this way should help to develop your understanding by appreciating the practical application and significance of what you read, and make your studies relevant to your personal development at work. It should also provide you with examples which can be used in your examination answers. And finally … We hope you enjoy your studies and find them useful not just for preparing for the examination, but also in understanding the modern world of business and in developing in your own job. We wish you every success in your studies and in the examination for this unit. Published by: The Association of Business Executives 5th Floor, CI Tower St Georges Square New Malden Surrey KT3 4TE United Kingdom All our rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the Association of Business Executives (ABE). © The Association of Business Executives (ABE) 2011 © ABE vii © ABE viii Unit Specification (Syllabus) The following syllabus – learning objectives, assessment criteria and indicative content – for this Level 5 unit has been approved by the Qualifications and Credit Framework. Unit Title: Quantitative Methods for Business and Management Guided Learning Hours: 160 Level: Level 5 Number of Credits: 18 Learning Outcome 1 The learner will: Understand different types of numerical data and different data collection processes, and be able to present data effectively for users in business and management. Assessment Criteria Indicative Content The learner can: 1.1 Explain the main sources and 1.1.1 Explain the main sources and types of data types of data and distinguish (including primary and secondary data, discrete and between alternative sampling continuous data, quantitative and categorical data). methods and measurement 1.1.2 Compare and contrast alternative sampling scales. methods and explain the main features of surveys, questionnaire design and the concept of sampling error and bias. 1.1.3 Distinguish between alternative measurement scales (nominal, ordinal, interval and ratio scales). 1.2 Construct appropriate tables 1.2.1 Construct appropriate tables and charts, including and charts, and calculate and frequency and cumulative frequency distributions and interpret a set of descriptive their graphical representations. statistics. 1.2.2 Calculate and interpret measures of location, dispersion, relative dispersion and skewness for ungrouped and grouped data. 1.3 Compute and interpret index 1.3.1 Compute unweighted and weighted index numbers. numbers and understand their applications. 1.3.2 Change the base period of an index number series. Learning Outcome 2 The learner will: Understand the basic concepts of probability and probability distributions, and their applications in business and management. Assessment Criteria Indicative Content The learner can: 2.1 Demonstrate an understanding 2.1.1 Demonstrate an understanding of the basic rules of the basic rules of probability and of probability. probability distributions, and apply 2.1.2 Explain the conditions under which the binomial them to compute probabilities. and Poisson distributions may be used and apply them to compute probabilities. © ABE ix 2.1.3 Explain the characteristics of the normal distribution and apply it to compute probabilities. 2.2 Explain and discuss the 2.2.1 Explain and discuss the importance of sampling importance of sampling theory and theory and the sampling distribution of the mean. the central limit theorem and 2.2.2 Discuss the importance of the central limit related concepts. theorem. 2.2.3 Define the ‘standard error of the mean’. 2.3 Construct and interpret 2.3.1 Construct and interpret confidence intervals, using confidence intervals and conduct the normal or t distribution, as appropriate, and calculate hypothesis tests. the sample size required to estimate population values to within given limits. 2.3.2 Conduct hypothesis tests of a single mean, a single proportion, the difference between two means and the difference between two proportions. 2.3.3 Conduct chi-squared tests of goodness-of-fit and independence and interpret the results. Learning Outcome 3 The learner will: Understand how to apply statistical methods to investigate inter- relationships between, and patterns in, business variables. Assessment Criteria Indicative Content The learner can: 3.1 Construct scatter diagrams 3.1.1 Construct scatter diagrams to illustrate linear and calculate and interpret association between two variables and comment on the correlation coefficients between shape of the graph. business variables. 3.1.2 Calculate and interpret Pearson’s coefficient of correlation and Spearman’s ‘rank’ correlation coefficient and distinguish between correlation and causality. 3.2 Estimate regression 3.2.1 Estimate the regression line for a two-variable coefficients and make predictions. model and interpret the results from simple and multiple regression models. 3.2.2 Use an estimated regression equation to make predictions and comment on their likely accuracy. 3.3 Explain the variations in time- 3.3.1 Distinguish between the various components of a series data, estimate the trend and time series (trend, cyclical variation, seasonal variation seasonal factors in a time series and random variation). and make business forecasts. 3.3.2 Estimate a trend by applying the method of moving averages and simple linear regression. 3.3.3 Apply the additive and multiplicative models to estimate seasonal factors. 3.3.4 Use estimates of the trend and seasonal factors to forecast future values (and comment on their likely accuracy) and to compute seasonally-adjusted data © ABE x Learning Outcome 4 The learner will: Understand how statistics and mathematics can be applied in the solution of economic and business problems. Assessment Criteria Indicative Content The learner can: 4.1 Construct probability trees and 4.1.1 Explain and calculate expected monetary values decision trees and compute and and construct probability trees. interpret EMVs (Expected 4.1.2 Construct decision trees and show how they can Monetary Values) as an aid to be used as an aid to business decision-making in the business decision-making under face of uncertainty. conditions of uncertainty. 4.1.3 Discuss the limitations of EMV analysis in business decision-making. 4.2 Construct demand and supply 4.2.1 Use algebraic and graphical representations of functions to determine equilibrium demand and supply functions to determine the prices and quantities, and analyse equilibrium price and quantity in a competitive market. the effects of changes in the 4.2.2 Analyse the effects of changes in the market (e.g. market. the imposition of a sales tax) on the equilibrium price and quantity. 4.3 Apply, and explain the 4.3.1 Apply break-even analysis to determine the output limitations of, break-even analysis decisions of firms and to analyse the effects of changes to determine firms’ output in the cost and revenue functions. decisions, and analyse the effects 4.3.2 Discuss the importance and explain the limitations of cost and revenue changes. of simple break-even analysis. © ABE